140 lines
3.2 KiB
Go
140 lines
3.2 KiB
Go
/*
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Copyright © 2025 filifa
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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package cmd
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import (
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"fmt"
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"log"
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"math/big"
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"github.com/spf13/cobra"
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)
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var remainders []string
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var moduli []string
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func crtSolve(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
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// use Bezout's identity to find m1, m2 such that m1*n1 + m2*n2 = 1
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m1 := new(big.Int)
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m2 := new(big.Int)
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tmp := new(big.Int)
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tmp.GCD(m1, m2, n1, n2)
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// x = a1*m2*n2 + a2*m1*n1
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x := new(big.Int).Set(a1)
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x.Mul(x, m2)
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x.Mul(x, n2)
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tmp.Set(a2)
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tmp.Mul(tmp, m1)
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tmp.Mul(tmp, n1)
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x.Add(x, tmp)
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N := new(big.Int).Set(n1)
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N.Mul(N, n2)
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x.Mod(x, N)
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return x, N
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}
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func arePairwiseCoprime(moduli []*big.Int) bool {
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z := new(big.Int)
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for i, a := range moduli {
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for _, b := range moduli[i+1:] {
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z.GCD(nil, nil, a, b)
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if z.Cmp(big.NewInt(1)) != 0 {
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return false
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}
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}
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}
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return true
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}
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func crt(cmd *cobra.Command, args []string) {
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if len(remainders) != len(moduli) {
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log.Fatal("number of remainders and moduli do not match")
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}
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ns := make([]*big.Int, len(moduli))
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for i := range moduli {
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n, ok := new(big.Int).SetString(moduli[i], 10)
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if !ok {
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log.Fatal("invalid input " + moduli[i])
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}
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ns[i] = new(big.Int).Set(n)
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}
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// TODO: support non-pairwise coprime moduli
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if !arePairwiseCoprime(ns) {
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log.Fatalf("moduli %v are not pairwise coprime", moduli)
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}
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n1 := new(big.Int)
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a1 := new(big.Int)
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for i, n2 := range ns {
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a2, ok := new(big.Int).SetString(remainders[i], 10)
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if !ok {
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log.Fatal("invalid input " + remainders[i])
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}
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if i == 0 {
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a1.Set(a2)
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n1.Set(n2)
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continue
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}
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x, N := crtSolve(a1, n1, a2, n2)
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a1.Set(x)
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n1.Set(N)
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}
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fmt.Println(a1)
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fmt.Println(n1)
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}
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// crtCmd represents the crt command
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var crtCmd = &cobra.Command{
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Use: "crt -r R R [R ...] -m M M [M ...]",
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Short: "Solve a system of linear congruences",
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Long: `Solve a system of linear congruences.`,
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Run: crt,
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}
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func init() {
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rootCmd.AddCommand(crtCmd)
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// Here you will define your flags and configuration settings.
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// Cobra supports Persistent Flags which will work for this command
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// and all subcommands, e.g.:
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// crtCmd.PersistentFlags().String("foo", "", "A help for foo")
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// Cobra supports local flags which will only run when this command
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// is called directly, e.g.:
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// crtCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
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crtCmd.Flags().StringSliceVarP(&remainders, "remainders", "r", make([]string, 0), "remainders of congruences")
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crtCmd.MarkFlagRequired("remainders")
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crtCmd.Flags().StringSliceVarP(&moduli, "moduli", "m", make([]string, 0), "moduli of congruences")
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crtCmd.MarkFlagRequired("moduli")
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}
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